Oil spills at sea pose a serious threat to coastal environments. Identifying oil pollution sources could help to investigate unreported spills, and satellite imagery can be an effective tool for this purpose. We present a Bayesian approach to estimate the source parameters of a spill from contours of oil slicks detected by remotely sensed images. Five parameters of interest are estimated: the 2D coordinates of the source of release, the time and duration of the spill, and the quantity of oil released. Two synthetic experiments of a spill released from a fixed point source are investigated, where a contour is fully observed in the first case, while two contours are partially observed at two different times in the second. In both experiments, the proposed method is able to provide good estimates of the parameters along with a level of confidence reflected by the uncertainties within.